The partial pressure of CO2 inside a bottle of soft drink is 4.0 atm at 25°C. The solubility of CO2 is 0.12 mol/L. When the bottle is opened, the partial pressure drops to 3.0 ✕ 10-4 atm. What is the solubility of CO2 in the open drink? Express your answer in grams per liter.
Henry's Law says concn is proportional to pressure; therefore,
0.12 x (3E-4/4) = ? M = ? mols/L.
Convert to grams/L.
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To find the solubility of CO2 in the open drink, we can use Henry's Law, which states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
Henry's Law equation is:
C = k * P
Where:
C is the molar concentration of the gas in the liquid
k is the Henry's Law constant
P is the partial pressure of the gas above the liquid
Let's calculate the molar concentration of CO2 in the closed bottle using Henry's Law:
C_closed = k * P_closed
C_closed = (0.12 mol/L/atm) * (4.0 atm)
C_closed = 0.48 mol/L
Now, let's calculate the molar concentration of CO2 in the open drink:
C_open = k * P_open
C_open = C_closed * (P_open / P_closed)
C_open = 0.48 mol/L * (3.0 * 10^-4 atm / 4.0 atm)
C_open = 3.6 * 10^-5 mol/L
Finally, we need to convert the molar concentration to grams per liter by multiplying by the molar mass of CO2:
Molar mass of CO2 = 44.01 g/mol
Solubility of CO2 in the open drink = C_open * Molar mass of CO2
Solubility of CO2 in the open drink = (3.6 * 10^-5 mol/L) * (44.01 g/mol)
Solubility of CO2 in the open drink = 0.001584 g/L
Therefore, the solubility of CO2 in the open drink is 0.001584 grams per liter.
To find the solubility of CO2 in the open drink, we need to calculate the change in concentration of CO2 using the change in partial pressure.
The solubility of CO2 is given in mol/L, so we need to convert the partial pressure to concentration using the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
First, let's convert the given temperatures from Celsius to Kelvin:
25°C + 273.15 = 298.15 K
Now, let's calculate the initial concentration of CO2 using the given partial pressure and solubility:
Partial pressure of CO2 = 4.0 atm
Solubility of CO2 = 0.12 mol/L
Using PV = nRT, we can rearrange the equation to solve for n/V (concentration):
n/V = P / RT
n/V = 4.0 atm / (0.0821 L.atm/mol.K * 298.15 K)
n/V = 0.163 mol/L
So, the initial concentration of CO2 in the closed bottle is 0.163 mol/L.
Next, let's calculate the final concentration of CO2 in the open drink using the change in partial pressure:
Partial pressure of CO2 in open drink = 3.0 × 10^-4 atm
Using PV = nRT, we can rearrange the equation to solve for n/V (concentration):
n/V = P / RT
n/V = (3.0 × 10^-4 atm) / (0.0821 L.atm/mol.K * 298.15 K)
n/V = 1.21 × 10^-6 mol/L
So, the final concentration of CO2 in the open drink is 1.21 × 10^-6 mol/L.
To convert the concentration from mol/L to g/L, we need to multiply by the molar mass of CO2 (44.01 g/mol):
(1.21 × 10^-6 mol/L) * (44.01 g/mol) = 5.33 × 10^-5 g/L
So, the solubility of CO2 in the open drink is 5.33 × 10^-5 g/L.